The hair cycle normally consists of growing, resting and falling hairs and there is a delicate balance between these stages of hair cycle. Normally hair should re-grow but if it is not happening, you should consider seeing a dermatologist. Egg in take and how to eat it depends on your blood cholesterol levels, if your reports are normal eat the whole egg.
Further authentic information is in the following weblink https://www.aad.org/public/diseases/hair-and-scalp-problems/hair-loss
Start on biotin supplements and food rich in iron content. Use a milder shampoo and consider frequent shampooing and conditioning.